Internal problem ID [1985]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number: Problem 14.5 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {\left (y^{3}+x \right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 260
dsolve((x+y(x)^3)*diff(y(x),x)=y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (27 x +3 \sqrt {24 c_{1}^{3}+81 x^{2}}\right )^{\frac {1}{3}}}{3}-\frac {2 c_{1}}{\left (27 x +3 \sqrt {24 c_{1}^{3}+81 x^{2}}\right )^{\frac {1}{3}}} \\ y \relax (x ) = -\frac {\left (27 x +3 \sqrt {24 c_{1}^{3}+81 x^{2}}\right )^{\frac {1}{3}}}{6}+\frac {c_{1}}{\left (27 x +3 \sqrt {24 c_{1}^{3}+81 x^{2}}\right )^{\frac {1}{3}}}-\frac {i \sqrt {3}\, \left (\frac {\left (27 x +3 \sqrt {24 c_{1}^{3}+81 x^{2}}\right )^{\frac {1}{3}}}{3}+\frac {2 c_{1}}{\left (27 x +3 \sqrt {24 c_{1}^{3}+81 x^{2}}\right )^{\frac {1}{3}}}\right )}{2} \\ y \relax (x ) = -\frac {\left (27 x +3 \sqrt {24 c_{1}^{3}+81 x^{2}}\right )^{\frac {1}{3}}}{6}+\frac {c_{1}}{\left (27 x +3 \sqrt {24 c_{1}^{3}+81 x^{2}}\right )^{\frac {1}{3}}}+\frac {i \sqrt {3}\, \left (\frac {\left (27 x +3 \sqrt {24 c_{1}^{3}+81 x^{2}}\right )^{\frac {1}{3}}}{3}+\frac {2 c_{1}}{\left (27 x +3 \sqrt {24 c_{1}^{3}+81 x^{2}}\right )^{\frac {1}{3}}}\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.949 (sec). Leaf size: 227
DSolve[(x+y[x]^3)*y'[x]==y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2\ 3^{2/3} c_1-\sqrt [3]{3} \left (-9 x+\sqrt {81 x^2+24 c_1{}^3}\right ){}^{2/3}}{3 \sqrt [3]{-9 x+\sqrt {81 x^2+24 c_1{}^3}}} \\ y(x)\to \frac {-(-1)^{2/3} \left (-9 x+\sqrt {81 x^2+24 c_1{}^3}\right ){}^{2/3}-2 \sqrt [3]{-3} c_1}{3^{2/3} \sqrt [3]{-9 x+\sqrt {81 x^2+24 c_1{}^3}}} \\ y(x)\to \frac {2 \sqrt [3]{-3} \left (-9 x+\sqrt {81 x^2+24 c_1{}^3}\right ){}^{2/3}+4 (-3)^{2/3} c_1}{6 \sqrt [3]{-9 x+\sqrt {81 x^2+24 c_1{}^3}}} \\ y(x)\to 0 \\ \end{align*}